This project is concerned with developing new statistical methodology for population genetic data. Attention will be focused on dependencies among sets of alleles: the applications of Hardy-Weinberg testing in high-dimensional genetic data and the characterization of population structure with rare variants and related populations. Theory will be developed at least in part in response to the needs of current whole-genome SNP surveys and whole-genome sequence variant surveys for humans. This work will be extended to analyses of population structure and ancestry proportions to the intensely selected and medically important HLA region to provide an in-depth analysis of population structure and ancestry proportions. The work is proposed by investigators in the Department of Biostatistics at the University of Washington. They will be joined by Jerome Goudet at the University of Lausanne, Jan Graffelman at the Universitat Politecnica de Catalunya and Diogo Meyer at the University of Sao Paulo.